5 25 27 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 25   c = 27

Area: T = 59.29774493549
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 10.11991720527° = 10°7'9″ = 0.17766128699 rad
Angle ∠ B = β = 61.46596345151° = 61°27'35″ = 1.07326729794 rad
Angle ∠ C = γ = 108.4211193432° = 108°25'16″ = 1.89223068043 rad

Height: ha = 23.7198979742
Height: hb = 4.74437959484
Height: hc = 4.39224036559

Median: ma = 25.89988416729
Median: mb = 14.85876579581
Median: mc = 11.94878031453

Inradius: r = 2.08106122581
Circumradius: R = 14.22991111874

Vertex coordinates: A[27; 0] B[0; 0] C[2.38988888889; 4.39224036559]
Centroid: CG[9.79662962963; 1.4644134552]
Coordinates of the circumscribed circle: U[13.5; -4.49663991352]
Coordinates of the inscribed circle: I[3.5; 2.08106122581]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.8810827947° = 169°52'51″ = 0.17766128699 rad
∠ B' = β' = 118.5440365485° = 118°32'25″ = 1.07326729794 rad
∠ C' = γ' = 71.57988065678° = 71°34'44″ = 1.89223068043 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 5 ; ; b = 25 ; ; c = 27 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 5+25+27 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-5)(28.5-25)(28.5-27) } ; ; T = sqrt{ 3516.19 } = 59.3 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.3 }{ 5 } = 23.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.3 }{ 25 } = 4.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.3 }{ 27 } = 4.39 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 5**2-25**2-27**2 }{ 2 * 25 * 27 } ) = 10° 7'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-5**2-27**2 }{ 2 * 5 * 27 } ) = 61° 27'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-5**2-25**2 }{ 2 * 25 * 5 } ) = 108° 25'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.3 }{ 28.5 } = 2.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 10° 7'9" } = 14.23 ; ;




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